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Solve for x. Enter the solutions from least to greatest. 2x^(2)-5=13 lesser x= greater x=

Solve for x x .\newlineEnter the solutions from least to greatest.\newline2x2−5=13 2 x^{2}-5=13 \newlinelesser x= x= \newlinegreater x= x=

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Full solution

Q. Solve for x x .\newlineEnter the solutions from least to greatest.\newline2x2−5=13 2 x^{2}-5=13 \newlinelesser x= x= \newlinegreater x= x=
  1. Isolate x2x^2 term: The question prompt is: ＂Solve for xx where 2x2−5=132x^2 - 5 = 13.＂\newlineFirst, we need to isolate the x2x^2 term by moving the constant term to the other side of the equation.\newline2x2−5+5=13+52x^2 - 5 + 5 = 13 + 5\newline2x2=182x^2 = 18
  2. Divide by 22: Next, we divide both sides of the equation by 22 to solve for x2x^2.\newline2x22=182\frac{2x^2}{2} = \frac{18}{2}\newlinex2=9x^2 = 9
  3. Take square root: Now, we take the square root of both sides to solve for x. Remember that taking the square root of a number yields two solutions: one positive and one negative.\newlinex2=±9\sqrt{x^2} = \pm\sqrt{9}\newlinex = ±3\pm3
  4. Two solutions for x: We have found two solutions for x. The lesser value is −3-3 and the greater value is 33.\newlinelesser x=−3x = -3\newlinegreater x=3x = 3

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